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Simplifying -9y2 + 18y + -12 = 6y Reorder the terms: -12 + 18y + -9y2 = 6y Solving -12 + 18y + -9y2 = 6y Solving for variable 'y'. Reorder the terms: -12 + 18y + -6y + -9y2 = 6y + -6y Combine like terms: 18y + -6y = 12y -12 + 12y + -9y2 = 6y + -6y Combine like terms: 6y + -6y = 0 -12 + 12y + -9y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 4y + -3y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 4y + -3y2)' equal to zero and attempt to solve: Simplifying -4 + 4y + -3y2 = 0 Solving -4 + 4y + -3y2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.333333333 + -1.333333333y + y2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -1.333333333y + -1.333333333 + y2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -1.333333333y + y2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -1.333333333y + y2 = 0 + -1.333333333 -1.333333333y + y2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -1.333333333y + y2 = -1.333333333 The y term is -1.333333333y. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333y + 0.4444444442 + y2 = -1.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333y + y2 = -1.333333333 + 0.4444444442 Combine like terms: -1.333333333 + 0.4444444442 = -0.8888888888 0.4444444442 + -1.333333333y + y2 = -0.8888888888 Factor a perfect square on the left side: (y + -0.6666666665)(y + -0.6666666665) = -0.8888888888 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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